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Lecture
Turing Machines: Decidability and Recursion Theory
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Formal Definition of Turing Machines
Explores the theoretical definition of computation and introduces Turing machines.
Theory of Computability and Halting Problem
Covers the theory of computability and the halting problem in algorithms.
Halting Problem: Unsolvable Problems
Explores the halting problem, demonstrating its unsolvability and the limitations of algorithms.
Turing Machine Example: Testing for Even Numbers
Demonstrates a Turing machine testing for even numbers using binary input.
Theory of Computation: Decidability and Complexity
Delves into the theory of computation, covering decidability, complexity, P vs. NP, and reductions.
Dynamics of Steady Euler Flows: New Results
Explores the dynamics of steady Euler flows on Riemannian manifolds, covering ideal fluids, Euler equations, Eulerisable flows, and obstructions to exhibiting plugs.
Computational Complexity
Covers the basics of computational complexity, including big O notation and complexity classes.
Theory of Computation: Undecidable Problems
Explores the existence of functions that cannot be computed, illustrated by famous paradoxes and the concept of undecidable problems.
Theory of Computability: Solvability and Complexity
Explores the theory of computability, decision problems, complexity classes, and the 'P vs. NP' conundrum.
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